Download Basic Business Statistics, 8th edition

Basic Business Statistics
(8th Edition)
Introduction and Data Collection
© 2002 Prentice-Hall, Inc.
Chap 1-1
Chapter Topics


Why a manager needs to know about
statistics
The growth and development of modern
statistics

Key definitions

Descriptive versus inferential statistics
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-2
Chapter Topics

Why data are needed

Types of data and their sources

Design of survey research

Types of sampling methods

Types of survey errors
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
(continued)
Chap 1-3
Why a Manager Needs to
Know about Statistics




To know how to properly present
information
To know how to draw conclusions
about populations based on sample
information
To know how to improve processes
To know how to obtain reliable
forecasts
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-4
The Growth and Development
of Modern Statistics
Needs of government to
collect data on its citizens
The development of the
mathematics of probability
theory
The advent of the computer
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-5
Key Definitions




A population (universe) is the collection of
things under consideration
A sample is a portion of the population
selected for analysis
A parameter is a summary measure
computed to describe a characteristic of the
population
A statistic is a summary measure computed
to describe a characteristic of the sample
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-6
Population and Sample
Population
Sample
Use statistics to
summarize features
Use parameters to
summarize features
Inference on the population from the sample
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-7
Statistical Methods

Descriptive statistics


Collecting and describing data
Inferential statistics

Drawing conclusions and/or making
decisions concerning a population based
only on sample data
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-8
Descriptive Statistics

Collect data


Present data


e.g. Survey
e.g. Tables and graphs
Characterize data

e.g. Sample mean =
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
X
i
n
Chap 1-9
Inferential Statistics

Estimation


e.g.: Estimate the population
mean weight using the
sample mean weight
Hypothesis testing

e.g.: Test the claim that the
population mean weight is
120 pounds
Drawing conclusions and/or making decisions
concerning a population based on sample results.
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-10
Why We Need Data

To provide input to survey

To provide input to study




To measure performance of service or
production process
To evaluate conformance to standards
To assist in formulating alternative courses
of action
To satisfy curiosity
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-11
Data Sources
Primary
Secondary
Data Collection
Data Compilation
Print or Electronic
Observation
Survey
Experimentation
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-12
Types of Data
Data
Categorical
(Qualitative)
Numerical
(Quantitative)
Discrete
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Continuous
Chap 1-13
Design of Survey Research

Choose an appropriate mode of response

Reliable primary modes




Personal interview
Telephone interview
Mail survey
Less reliable self-selection modes (not appropriate
for making inferences about the population)




Television survey
Internet survey
Printed survey on newspapers and magazines
Product or service questionnaires
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-14
Design of Survey Research
(continued)

Identify broad categories


Formulate accurate questions


List complete and non-overlapping categories
that reflect the theme
Make questions clear and unambiguous. Use
universally-accepted definitions
Test the survey

Pilot test the survey on a small group of
participants to assess clarity and length
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-15
Design of Survey Research
(continued)

Write a cover letter




State the goal and purpose of the survey
Explain the importance of a response
Provide assurance of respondent’s anonymity
Offer incentive gift for respondent participation
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-16
Reasons for Drawing a Sample

Less time consuming than a census

Less costly to administer than a census

Less cumbersome and more practical to
administer than a census of the targeted
population
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-17
Types of Sampling Methods
Samples
Non-Probability
Samples
Probability Samples
Simple
Random
Judgement
Chunk
Quota
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Stratified
Cluster
Systematic
Chap 1-18
Probability Sampling

Subjects of the sample are chosen based on
known probabilities
Probability Samples
Simple
Random
Systematic
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Stratified
Cluster
Chap 1-19
Simple Random Samples



Every individual or item from the frame has
an equal chance of being selected
Selection may be with replacement or without
replacement
Samples obtained from table of random
numbers or computer random number
generators
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-20
Systematic Samples




Decide on sample size: n
Divide frame of N individuals into groups of k
individuals: k=n/n
Randomly select one individual from the 1st
group
Select every k-th individual thereafter
N = 64
n=8
First Group
k=8
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-21
Stratified Samples



Population divided into two or more groups
according to some common characteristic
Simple random sample selected from each
group
The two or more samples are combined into
one
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-22
Cluster Samples

Population divided into several “clusters,”
each representative of the population

Simple random sample selected from each

The samples are combined into one
Population
divided
into 4
clusters.
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-23
Advantages and Disadvantages

Simple random sample and systematic sample



Stratified sample


Simple to use
May not be a good representation of the
population’s underlying characteristics
Ensures representation of individuals across the
entire population
Cluster sample


More cost effective
Less efficient (need larger sample to acquire the
same level of precision)
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-24
Evaluating Survey Worthiness






What is the purpose of the survey?
Is the survey based on a probability sample?
Coverage error – appropriate frame
Nonresponse error – follow up
Measurement error – good questions elicit
good responses
Sampling error – always exists
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-25
Types of Survey Errors

Coverage error
Excluded from
frame.

Non response error
Follow up on
non responses.

Sampling error

Measurement error
Chance
differences from
sample to sample.
Bad Question!
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-26
Chapter Summary




Addressed why a manager needs to know
about statistics
Discussed the growth and development of
modern statistics
Addressed the notion of descriptive versus
inferential statistics
Discussed the importance of data
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-27
Chapter Summary




(continued)
Defined and described the different types of
data and sources
Discussed the design of survey
Discussed types of sampling methods
Described different types of survey errors
Basic Business Statistics, 8e © 2002 Prentice-Hall, Inc.
Chap 1-28
Basic Business Statistics
(8th Edition)
Presenting Data in
Tables and Charts
© 2002 Prentice-Hall, Inc.
Chap 2-29
Chapter Topics

Organizing numerical data


Tabulating and graphing Univariate numerical
data



The ordered array and stem-leaf display
Frequency distributions: tables, histograms,
polygons
Cumulative distributions: tables, the Ogive
Graphing Bivariate numerical data
© 2002 Prentice-Hall, Inc.
Chap 2-30
Chapter Topics



Tabulating and graphing Univariate
categorical data

The summary table

Bar and pie charts, the Pareto diagram
(continued)
Tabulating and graphing Bivariate categorical
data

Contingency tables

Side by side bar charts
Graphical excellence and common errors in
presenting data
© 2002 Prentice-Hall, Inc.
Chap 2-31
Organizing Numerical Data
Numerical Data
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem and Leaf
Display
© 2002 Prentice-Hall, Inc.
2 144677
3 028
4 1
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
Cumulative Distributions
Histograms
Tables
Ogive
Polygons
Chap 2-32
Organizing Numerical Data
(continued)



Data in raw form (as collected):
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Data in ordered array from smallest to largest:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem-and-leaf display:
2 144677
3 028
4 1
© 2002 Prentice-Hall, Inc.
Chap 2-33
Tabulating and Graphing
Numerical Data
Numerical Data
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
Cumulative Distributions
O g ive
120
100
80
60
40
20
0
10
Stem and Leaf
Display
2 144677
3 028
4 1
Histograms
30
40
50
60
Ogive
7
6
5
4
Tables
Polygons
3
2
1
0
10
© 2002 Prentice-Hall, Inc.
20
20
30
40
50
60
Chap 2-34
Tabulating Numerical Data:
Frequency Distributions

Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find range: 58 - 12 = 46

Select number of classes: 5 (usually between 5 and 15)

Compute class interval (width): 10 (46/5 then round up)

Determine class boundaries (limits):

Compute class midpoints:

Count observations & assign to classes
© 2002 Prentice-Hall, Inc.
10, 20, 30, 40, 50, 60
15, 25, 35, 45, 55
Chap 2-35
Frequency Distributions, Relative Frequency
Distributions and Percentage Distributions
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
10 but under 20
20 but under 30
30 but under 40
40 but under 50
50 but under 60
Total
© 2002 Prentice-Hall, Inc.
Relative
Frequency Frequency Percentage
3
6
5
4
2
20
.15
.30
.25
.20
.10
1
15
30
25
20
10
100
Chap 2-36
Graphing Numerical Data:
The Histogram
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Frequency
Histogram
7
6
5
4
3
2
1
0
6
5
3
2
0
5
Class Boundaries
© 2002 Prentice-Hall, Inc.
No Gaps
Between
Bars
4
0
15
25
36
45
Class Midpoints
55
More
Chap 2-37
Graphing Numerical Data:
The Frequency Polygon
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Frequenc y
7
6
5
4
3
2
1
0
5
© 2002 Prentice-Hall, Inc.
15
25
36
45
55
Class Midpoints
M ore
Chap 2-38
Tabulating Numerical Data:
Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
10 but under 20
20 but under 30
30 but under 40
40 but under 50
50 but under 60
© 2002 Prentice-Hall, Inc.
Cumulative
Frequency
3
9
14
18
20
Cumulative
% Frequency
15
45
70
90
100
Chap 2-39
Graphing Numerical Data:
The Ogive (Cumulative % Polygon)
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Ogive
100
80
60
40
20
0
10
20
30
40
50
60
Class Boundaries (Not Midpoints)
© 2002 Prentice-Hall, Inc.
Chap 2-40
Graphing Bivariate Numerical
Data (Scatter Plot)
Mutual Funds Scatter Plot
Total Year to
Date Return
(%)
40
30
20
10
0
0
© 2002 Prentice-Hall, Inc.
10
20
30
Net Asset Values
40
Chap 2-41
Tabulating and Graphing
Categorical Data:Univariate Data
Categorical Data
Tabulating Data
The Summary Table
Graphing Data
Pie Charts
Bar Charts
© 2002 Prentice-Hall, Inc.
Pareto Diagram
Chap 2-42
Summary Table
(for an Investor’s Portfolio)
Investment Category
Amount
Percentage
(in thousands $)
Stocks
Bonds
CD
Savings
Total
46.5
32
15.5
16
110
42.27
29.09
14.09
14.55
100
Variables are Categorical
© 2002 Prentice-Hall, Inc.
Chap 2-43
Graphing Categorical Data:
Univariate Data
Categorical Data
Graphing Data
Tabulating Data
The Summary Table
Pie Charts
CD
Pareto Diagram
S a vi n g s
Bar Charts
B onds
S to c k s
0
10
20
30
40
50
45
120
40
100
35
30
80
25
60
20
15
40
10
20
5
0
0
S to c k s
© 2002 Prentice-Hall, Inc.
B onds
S a vi n g s
CD
Chap 2-44
Bar Chart
(for an Investor’s Portfolio)
Investor's Portfolio
Savings
CD
Bonds
Stocks
0
10
20
30
40
50
Amount in K$
© 2002 Prentice-Hall, Inc.
Chap 2-45
Pie Chart
(for an Investor’s Portfolio)
Amount Invested in K$
Savings
15%
Stocks
42%
CD
14%
Bonds
29%
© 2002 Prentice-Hall, Inc.
Percentages are
rounded to the
nearest percent.
Chap 2-46
Pareto Diagram
Axis for
bar
chart
shows
%
invested
in each
category
45%
100%
40%
90%
80%
35%
70%
30%
60%
25%
50%
20%
40%
15%
30%
10%
20%
5%
10%
0%
0%
Stocks
© 2002 Prentice-Hall, Inc.
Bonds
Savings
Axis for line
graph
shows
cumulative
% invested
CD
Chap 2-47
Tabulating and Graphing
Bivariate Categorical Data

Contingency tables:
Investment
Category
Investor A
Stocks
Bonds
CD
Savings
46.5
32
15.5
16
Total
110
© 2002 Prentice-Hall, Inc.
investment in thousands of dollars
Investor B
Investor C
Total
55
44
20
28
27.5
19
13.5
7
129
95
49
51
147
67
324
Chap 2-48
Tabulating and Graphing
Bivariate Categorical Data

Side by side charts
C o m p arin g In vesto rs
S avings
CD
B onds
S toc k s
0
10
Inves tor A
© 2002 Prentice-Hall, Inc.
20
30
Inves tor B
40
50
60
Inves tor C
Chap 2-49
Principles of Graphical Excellence





Presents data in a way that provides
substance, statistics and design
Communicates complex ideas with clarity,
precision and efficiency
Gives the largest number of ideas in the most
efficient manner
Almost always involves several dimensions
Tells the truth about the data
© 2002 Prentice-Hall, Inc.
Chap 2-50
Errors in Presenting Data


Using “chart junk”
Failing to provide a relative
basis in comparing data
between groups

Compressing the vertical axis

Providing no zero point on the vertical axis
© 2002 Prentice-Hall, Inc.
Chap 2-51
“Chart Junk”
Bad Presentation
 Good Presentation
Minimum Wage
1960: $1.00
Minimum Wage
4
$
1970: $1.60
2
1980: $3.10
0
1990: $3.80
© 2002 Prentice-Hall, Inc.
1960
1970
1980
1990
Chap 2-52
No Relative Basis
Bad Presentation
 Good Presentation
A’s received by
Freq. students.
300
200
30 %

10
0

FR SO
JR SR
A’s received by
students.

FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
© 2002 Prentice-Hall, Inc.
Chap 2-53
Compressing Vertical Axis
Bad Presentation
Good Presentation
Quarterly Sales
200
$
Quarterly Sales
50
100
25
0
0
Q1 Q2
© 2002 Prentice-Hall, Inc.
Q3 Q4
$
Q1
Q2
Q3 Q4
Chap 2-54
No Zero Point on Vertical Axis
Bad Presentation

Good Presentation
Monthly Sales
45
$
Monthly Sales
42
39
45
42
39
$
36
36
J F M A M J
0
J F M A M J
Graphing the first six months of sales.
© 2002 Prentice-Hall, Inc.
Chap 2-55
Chapter Summary

Organized numerical data


Tabulated and graphed univariate numerical
data



The ordered array and stem-leaf display
Frequency distributions: tables, histograms,
polygon
Cumulative distributions: tables and the Ogive
Graphed bivariate numerical data
© 2002 Prentice-Hall, Inc.
Chap 2-56
Chapter Summary

Tabulated and graphed univariate categorical
data



The summary table
Bar and pie charts, the Pareto diagram
Tabulated and graphed bivariate categorical
data



(continued)
Contingency tables
Side by side charts
Discussed graphical excellence and common
errors in presenting data
© 2002 Prentice-Hall, Inc.
Chap 2-57
Basic Business Statistics
(8th Edition)
Numerical Descriptive Measures
© 2002 Prentice-Hall, Inc.
Chap 3-58
Chapter Topics

Measures of central tendency

Mean, median, mode, geometric mean, midrange

Quartile

Measure of variation


Range, Interquartile range, variance and standard
deviation, coefficient of variation
Shape

Symmetric, skewed, using box-and-whisker plots
© 2002 Prentice-Hall, Inc.
Chap 3-59
Chapter Topics


(continued)
Coefficient of correlation
Pitfalls in numerical descriptive measures and
ethical considerations
© 2002 Prentice-Hall, Inc.
Chap 3-60
Summary Measures
Summary Measures
Central Tendency
Mean
Quartile
Mode
Median
Range
Variation
Coefficient of
Variation
Variance
Geometric Mean
© 2002 Prentice-Hall, Inc.
Standard Deviation
Chap 3-61
Measures of Central Tendency
Central Tendency
Average
Median
Mode
n
X 
X
i 1
N

i 1
Geometric Mean
X G   X1  X 2 
n
X
i
 Xn 
1/ n
i
N
© 2002 Prentice-Hall, Inc.
Chap 3-62
Mean (Arithmetic Mean)

Mean (arithmetic mean) of data values

Sample mean
Sample Size
n
X

X
i 1
i
n
 Xn
Population mean
Population Size
N

© 2002 Prentice-Hall, Inc.
X1  X 2 

n
X
i 1
N
i
X1  X 2 

N
 XN
Chap 3-63
Mean (Arithmetic Mean)
(continued)


The most common measure of central
tendency
Affected by extreme values (outliers)
0 1 2 3 4 5 6 7 8 9 10
Mean = 5
© 2002 Prentice-Hall, Inc.
0 1 2 3 4 5 6 7 8 9 10 12 14
Mean = 6
Chap 3-64
Median


Robust measure of central tendency
Not affected by extreme values
0 1 2 3 4 5 6 7 8 9 10
Median = 5

0 1 2 3 4 5 6 7 8 9 10 12 14
Median = 5
In an ordered array, the median is the
“middle” number


If n or N is odd, the median is the middle number
If n or N is even, the median is the average of the
two middle numbers
© 2002 Prentice-Hall, Inc.
Chap 3-65
Mode






A measure of central tendency
Value that occurs most often
Not affected by extreme values
Used for either numerical or categorical data
There may may be no mode
There may be several modes
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mode = 9
© 2002 Prentice-Hall, Inc.
0 1 2 3 4 5 6
No Mode
Chap 3-66
Geometric Mean

Useful in the measure of rate of change of a
variable over time
X G   X1  X 2 

 Xn 
1/ n
Geometric mean rate of return

Measures the status of an investment over time
RG  1  R1   1  R2  
© 2002 Prentice-Hall, Inc.
 1  Rn  
1/ n
1
Chap 3-67
Example
An investment of $100,000 declined to $50,000 at the
end of year one and rebounded to $100,000 at end of
year two:
X1  $100,000
X 2  $50,000
X 3  $100,000
Average rate of return:
(50%)  (100%)
X
 25%
2
Geometric rate of return:
RG  1   50%    1  100%   
1/ 2
  0.50    2  
1/ 2
© 2002 Prentice-Hall, Inc.
1
 1  1  1  0%
1/ 2
Chap 3-68
Quartiles

Split Ordered Data into 4 Quarters
25%
25%
 Q1 

25%
 Q2 
Position of i-th Quartile
25%
Q3 
i  n  1
 Qi  
4
Data in Ordered Array: 11 12 13 16 16 17 18 21 22
1 9  1
Position of Q1 
 2.5
4
Q1
12  13


 12.5
2
Q1 and Q3 Are Measures of Noncentral Location
 Q = Median, A Measure of Central Tendency
2

© 2002 Prentice-Hall, Inc.
Chap 3-69
Measures of Variation
Variation
Variance
Range
Population
Variance
Sample
Variance
Interquartile Range
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Standard Deviation
Coefficient
of Variation
Population
Standard
Deviation
Sample
Standard
Deviation
Chap 3-70
Range


Measure of variation
Difference between the largest and the
smallest observations:
Range  X Largest  X Smallest

Ignores the way in which data are distributed
Range = 12 - 7 = 5
Range = 12 - 7 = 5
7
8
© 2002 Prentice-Hall, Inc.
9
10
11
12
7
8
9
10
11
12
Chap 3-71
Interquartile Range


Measure of variation
Also known as midspread


Spread in the middle 50%
Difference between the first and third
quartiles
Data in Ordered Array: 11 12 13 16 16 17
17 18 21
Interquartile Range  Q3  Q1  17.5  12.5  5

Not affected by extreme values
© 2002 Prentice-Hall, Inc.
Chap 3-72
Variance


Important measure of variation
Shows variation about the mean

Sample variance:
n
S 
2

 X
i 1
X
i
2
n 1
Population variance:
N
 
2
© 2002 Prentice-Hall, Inc.
 X
i 1
i

N
2
Chap 3-73
Standard Deviation



Most important measure of variation
Shows variation about the mean
Has the same units as the original data

Sample standard deviation:
n
S

Population standard deviation:

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 X
i 1
X
i
2
n 1
N
 X
i 1
i

2
N
Chap 3-74
Comparing Standard Deviations
Data A
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
s = 3.338
Data B
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
s = .9258
Data C
11 12 13 14 15 16 17 18 19 20 21
© 2002 Prentice-Hall, Inc.
Mean = 15.5
s = 4.57
Chap 3-75
Coefficient of Variation

Measures relative variation

Always in percentage (%)

Shows variation relative to mean


Is used to compare two or more sets of data
measured in different units
S
CV  
X
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
100%

Chap 3-76
Comparing Coefficient
of Variation

Stock A:



Stock B:



Average price last year = $50
Standard deviation = $5
Average price last year = $100
Standard deviation = $5
Coefficient of variation:

Stock A:

Stock B:
© 2002 Prentice-Hall, Inc.
S
CV  
X

 $5 
100%  
100%  10%

 $50 
S
CV  
X

 $5 
100%  
100%  5%

 $100 
Chap 3-77
Shape of a Distribution

Describes how data is distributed

Measures of shape

Symmetric or skewed
Left-Skewed
Mean < Median < Mode
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Symmetric
Mean = Median =Mode
Right-Skewed
Mode < Median < Mean
Chap 3-78
Exploratory Data Analysis

Box-and-whisker plot

Graphical display of data using 5-number summary
X smallest Q
1
4
© 2002 Prentice-Hall, Inc.
6
Median( Q2)
8
Q3
10
Xlargest
12
Chap 3-79
Distribution Shape and
Box-and-Whisker Plot
Left-Skewed
Q1
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Q2 Q3
Symmetric
Q1Q2Q3
Right-Skewed
Q1 Q2 Q3
Chap 3-80
Coefficient of Correlation

Measures the strength of the linear
relationship between two quantitative
variables
n
r
 X
i 1
n
 X
i 1
© 2002 Prentice-Hall, Inc.
i
i
 X Yi  Y 
X
2
n
 Y  Y 
i 1
2
i
Chap 3-81
Features of
Correlation Coefficient

Unit free

Ranges between –1 and 1



The closer to –1, the stronger the negative linear
relationship
The closer to 1, the stronger the positive linear
relationship
The closer to 0, the weaker any positive linear
relationship
© 2002 Prentice-Hall, Inc.
Chap 3-82
Scatter Plots of Data with
Various Correlation Coefficients
Y
Y
Y
X
r = -1
X
r = -.6
Y
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X
r=0
Y
r = .6
X
r=1
X
Chap 3-83
Pitfalls in
Numerical Descriptive Measures

Data analysis is objective


Should report the summary measures that best
meet the assumptions about the data set
Data interpretation is subjective

Should be done in fair, neutral and clear manner
© 2002 Prentice-Hall, Inc.
Chap 3-84
Ethical Considerations
Numerical descriptive measures:



Should document both good and bad results
Should be presented in a fair, objective and
neutral manner
Should not use inappropriate summary
measures to distort facts
© 2002 Prentice-Hall, Inc.
Chap 3-85
Chapter Summary

Described measures of central tendency

Mean, median, mode, geometric mean, midrange

Discussed quartile

Described measure of variation


Range, interquartile range, variance and standard
deviation, coefficient of variation
Illustrated shape of distribution

Symmetric, skewed, box-and-whisker plots
© 2002 Prentice-Hall, Inc.
Chap 3-86
Chapter Summary


(continued)
Discussed correlation coefficient
Addressed pitfalls in numerical descriptive
measures and ethical considerations
© 2002 Prentice-Hall, Inc.
Chap 3-87